Philosophy of cosmology - Ellis. ON THE PHILOSOPHY OF COSMOLOGY George Ellis

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1 ON THE PHILOSOPHY OF COSMOLOGY George Ellis 1. INTRODUCTION 1.1 UNIQUENESS OF THE UNIVERSE 1.2 USE OF MODELS IN DESCRIPTION 1.3 USE OF MODELS IN EXPLANATION 1.4 EPISTEMOLOGY AND ONTOLOGY 1.5 PHILOSOPHY AND COSMOLOGICAL ISSUES 2. UNDERSTANDING COSMOLOGY: BASIC ISSUES 2.1 LIMITS ON OBSERVATIONS 2.2 THE BASIC PROGRAMME 2.3 MAJOR QUESTIONS 3. TESTING ALTERNATIVES 3.1 ALTERNATIVE TOPOLOGIES 3.2 ANISOTROPIC (BIANCHI) MODES 3.3 DARK MATTER AND MODIFIED GRAVITY 3.4 DARK ENERGY AND INHOMOGENEITY 4 TESTING CONSISTENCY 4.1. AGES: IS THE UNIVERSE OLDER THAN ITS CONTENTS? 4.2. CBR-MATTER DIPOLE AGREEMENT 4.3. COSMIC DISTANCE-DUALITY RELATION 4.4. CBR TEMPERATURE AT A DISTANCE 4.5. PRIMORDIAL ELEMENT ABUNDANCES WITH DISTANCE 5 THE UNIQENESS OF THE UNIVERSE 5.1 THE PHILOSOPHY OF THE HISTORICAL SCIENCES 5.2 LAWS AND INITIAL CONDITIONS 6 MULTIVERSES: DENYING THE UNIQUENESS OF THE UNIVERSE 6.1 FINE TUNING: THE ANTHROPIC ISSUE 6.2 TESTABILITY 6.3 CRITERIA FOR A SCIENTIFIC THEORY 6.4 JUSTIFYING UNSEEN ENTITIES 7: PHYSICAL LAWS AND THE NATURES OF EXISTENCE 7.1 PHYSICAL AND NON-PHYSICAL REALITIES 7.2 PHYSICAL LAWS AT THE FUNDAMENTAL LEVEL 7.3 THE PHYSICS HORIZON 7.4 INFINITIES 8 DEEPER ISSUES 8.1 THE SCOPE OF ENQUIRY AND LIMITS OF SCIENCE 8.2 LIMITS TO MODELS AND THE RELATION TO MATHEMATICS 8.3 PHYSICAL DETERMINISM AND LIFE TODAY 8.4 CONTEXT AND TOP DOWN CAUSATION 8.5 POSSIBILITY SPACES AND THE NATURE OF CAUSATION 8.6 ULTIMATE CAUSATION AND EXISTENCE 9 REPRISE REFERENCES 1

2 ABSTRACT This paper is an overview of significant issues in the philosophy of cosmology, starting off by emphasizing the issue of the uniqueness of the universe and the way models are used in description and explanation. It then considers successively, basic issues (limits on observations, the basic programme, major questions in cosmology); testing alternatives; testing consistency; and implications of the uniqeness of the universe. It goes on to look at multiverses and the anthropic issue, in particular considering criteria for a scientific theory and justifying unseen entities, as well as the relation between physical laws and the natures of existence. In particular it emphasizes the existence of both physical and non-physical entities, limits on our knowledge of the relevant physics ( the physics horizon ), and the non-physical nature of claimed infinities. The final section looks briefly at deeper issues, commenting on the scope of enquiry of cosmological theory and the limits of science; limits to models; physical determinism and life today; possibility spaces and the nature of causation; and ultimate causation and existence. 2

3 1. INTRODUCTION ON THE PHILOSOPHY OF COSMOLOGY George Ellis Talk at Granada Meeting, 2011 Philosophy underlies our approaches to cosmology, even though it is usually just taken for granted and so not often explicitly explored. The core issue for the philosophy of cosmology 1 is, What constitutes an explanation in the context of cosmology? This has several specific aspects: What kinds of things are we trying to explain? What kinds of questions do we want our models to solve? Can we explain what is, by asking what else could be the case? How do we restrict explanatory models in cosmology when they are underdetermined by the data? How do we test if the kinds of explanation we are offering are valid? The answers depend crucially on our investigation framework: Do you want to tackle only technical issues, restricting attention to Physical cosmology?, or Do you want to deal with issues of meaning as well, extending the investigation to Big questions? This is the basic underlying choice we have to make, which shapes the questions that we ask. If we do enter the latter terrain, we need to consider How much of reality do our models take seriously? In some cases of the models used are very limited in scope, but they are being used to answer questions that are beyond their capacity. 2 Awareness of this issue may help us resist that temptation. In any case we should remember that philosophical considerations are necessarily part of the physics enterprise (Zinkernagel 2011). Even when dealing with apparently purely technical issues, there will be philosophical assumptions underlying what we are doing. 1.1 UNIQUENESS OF THE UNIVERSE The underlying basic problem in studying cosmology is the uniqueness of the universe (McCrea 1953, Munitz 1986, Ellis 2006). There is only one object to look at, and no similar objects to compare it with. Also there is no chance to rerun it in an experiment. This is what makes cosmology unique as a science, and underlies most of the problems discussed below. It is a unique historical science, where no direct experiments are possible on the object being investigated as a whole (although many are possible on parts or aspects of the whole.) 1 See for example Munitz (1962), Ellis (2006), Zinkernagel (2011), Butterfield (2012). 2 See commentary at 3

4 It is for this reason that we have to be exceptionally careful in analyzing the relation between data and models. We need to extract all the evidence we can, and check our models in all possible ways. Additionally, this uniqueness has implications for explanation and how we understand the nature of laws and chance in this context. These specific implications will be discussed in Section USE OF MODELS IN DESCRIPTION Explanation depends on our ideas of what exists, so is initially preceded by descriptive models based on observations; but these will then include descriptions of causal factors as envisaged by explanatory models, so the descriptive and causal models will not be independent. In any case, models of any physical system are always an idealization: they include some items while excluding others. The question How accurate are they? depends on the kind of question we wish to answer. So the first issue is, 1. What kinds of things will they describe? If the aim is just to deal with physical cosmology, the kinds of entities are fairly obvious (geometry, matter, fields). But then the issue is, 2. How general will they be? The majority of models used in cosmology are perturbed Friedmann-Lemaître- Robertson-Walker (FLRW) models. But if one wants to explore the whole range of models consistent with observations, or the range of possibilities that are the framework for what actually exists, this will not be enough (as I discuss below). Each model has a domain of validity in terms of what it includes and what it excludes; these should be stated clearly, and not exceeded when it is used n explanatory mode. In particular, there are always hidden averaging scales in physical descriptions. One should consider, 3. What scales of description are included? What detail will they encompass? The further core issue is, 4. How will the proposed models be tested? Many models used in cosmology make major claims about unobservable entities and regions. An issue we pursue below is to what degree such claims can be called scientific. 1.3 USE OF MODELS IN EXPLANATION But our models go beyond description: they aim at explanation. So the issue here is, 1. What kinds of causation do we envisage in cosmology? There are obvious astrophysical kinds of causation here. But cosmological claims often go further than that: they try to explain the very existence of the universe. The kinds of causation envisaged here test the limits of science. So a key issue is, What are the limits of our causal models? How far do we take explanation? Each causal model has a domain of validity - which should be stated clearly and not exceeded. We will be able to use testable physics up to some point, but after that we will be in the domain of speculation. A further key issue therefore is 2. To what degree are our proposed causal models testable? 4

5 Exploring the limits will necessarily at least to start with involve presently untestable proposals, but the problem arises if they will be in principle untestable for ever. Their status as scientific explanation will then be in question no matter how attractive they may be from some specific philosophical viewpoint. And as in the case of description, causal models will never be complete: they will always omit some part of the causal nexus, inter alia because that involves all scales from the smallest to the largest and as indicated in the last section, we cannot fully represent all the causal variables at play, let alone the interactions between them. Our models will represent some causal influences but not all. So as always 3. Don t confuse causal models with reality! They will always of necessity be partial descriptions of the whole. One should respect their limits. 1.4 EPISTEMOLOGY AND ONTOLOGY As in all cases of scientific explanation, in cosmology we are relating knowledge to an external reality, and the key scientific requirement is to test those models against what is actually out there by observational and experimental means. But our observational access to the vast distant domains of the universe is strictly limited. This means that our model building is underdetermined, because access to data is restricted in three crucial ways. Firstly, as we look to distant domains in the universe, we see what is there through photons that travel towards us at the speed of light; so we can t see things as they are today, we only get data about things as they were in the past. To understand what things are like today, we have to extrapolate from the observable past to the unobservable present; and that is a model-dependent exercise. Secondly, as we peer back into the past, because the observable part of the universe has been in existence only for a finite time, there are particle and visual horizons limiting our causal and visual contact with distant domains. We can only see out to matter that is presently about 42 billion light years distant; 3 the rest is unobservable for ever, except perhaps by means of cosmological neutrinos and gravitational waves both of which are extraordinarily difficult to detect. And their scope too is limited by associated horizons. We will never have access to data about most of the universe (except if we live in a `small universe, discussed in Section 3.1 below; but this is probably not the case). Thirdly, we are also faced with a physics horizon a limit to our ability to test the physics relevant to understanding processes in the early universe. Hence there are profound limits on our ability to test physically explanations of what was going on then. These three limitations will necessarily be central to any study of epistemology of cosmology; they will be very apparent in the discussion that follows. Finally one must as always take selection and detection effects into account, asking what exists that we cannot see? What do we not detect? These are crucial in determining what we actually see and measure. 3 This is three times the Hubble scale distance; that factor is because the universe is expanding. See Ellis and Rothman (1993) 5

6 1.5 PHILOSOPHY AND COSMOLOGICAL ISSUES Because of these limits of observability and testability, as emphasized by Jeremy Butterfield (2012), our cosmological models are underdetermined by observations: we have to make theoretical assumptions to get unique models, both as regards physics and geometry. That s one reason why philosophy is inevitable in the study of cosmology: even if this is not often explicitly recognized, it s part of the territory, even in studying purely physical cosmology. And even with as much data as one would like, and even if one could use this to fix our cosmological model uniquely, we would still be left with the task of interpreting this model. Even if underdetermination could be eliminated at the model level, this does not imply that there is no underdetermination at the level of interpretation - i.e. about what the model implies for our understanding of the world (see Section 2 of Zinkernagel 2011). Of course this is much more apparent in tackling foundational issues and big questions, which go beyond purely physical cosmology (both are considered below). Proclaiming that philosophy is useless or meaningless will not help: cosmologists necessarily to some degree indulge in it, whether they acknowledge this fact or not. Poorly thought out philosophy is still philosophy, but it is unsatisfactory. Rather than denying its significance, we should carefully consider the philosophy-cosmology relation and develop a philosophy of cosmology of adequate depth. 2. UNDERSTANDING COSMOLOGY: BASIC ISSUES 2.1 LIMITS ON OBSERVATIONS Not only is no direct experiment possible on the whole, or observations of similar entities; additionally, because of its vast scale, our ability to examine the nature of the one universe in which we exist is very restricted. In effect we can only see the universe from one spacetime event: here and now (see Figure 1). All we can see (on a cosmological scale) lies on a single past lightcone; hence our cosmological models are underdetermined by possible observations: we have to make theoretical assumptions to get unique models, both as regards physics and geometry. The observational situation is shown in Figure 1. Insert Figure 1: The basic observational situation Conformal coordinates are used so that fundamental world lines are vertical lines, surfaces of homogeneity are horizontal planes, and null cones are at ±45 o. Spatial distances are distorted but causal relations are as in flat spacetime. The start of the universe is at the bottom. The universe was opaque until the Last Scattering Surface (LSS), where radiation decoupled from matter, and propagated freely from then on as cosmic black body radiation, nowadays peaked in the microwave region at 2.75K. Our world line is at the centre of the diagram; the present event here and now is about 14 6

7 billion years after decoupling. We see a distant galaxy at the instant it crosses our past light cone. All events before the LSS are hidden from our view. As the LSS is where the freely propagating cosmic microwave background (CMB) originates, it contains the CMB 2-sphere we see when we measure temperature fluctuations in the CMB across the sky (Figure 2). The matter we see in this way is the furthest matter we can see by any electromagnetic radiation; hence it forms the visual horizon. The Hot Big Bang (HBB) epoch is from the end of inflation (extremely soon after the start of the universe) until decoupling at the LSS. Nucleosynthesis took place shortly after the start of the HBB epoch, and determined the primordial abundance of light elements in our region, which we can estimate from nearby stellar spectra. Insert Figure 2: CMB 2-sphere 2.2 THE BASIC PROGRAMME The basic program relies on two elements: seeing what is there (based in numerous observations deriving from new telescopes) and fitting parametrised perturbed FLRW models to this data. These models involve theory: causal models give physics explanations of the dynamics, through applying the Einstein field equations with suitable matter models. Note that one fits the parameters of both the background model and of the perturbation spectrum for different matter components; one is modeling what matter is here now, and how it got there. The basic ingredients of the resulting concordance model (Harrison 2000, Silk 2001, Dodelson 2003, Ellis 2006, Ells, Maartens and MacCallum 2012) are, An inflationary era prior to the hot big bang stage, including generation of a seed perturbation spectrum; The end of inflation, reheating, and baryosynthesis; The Hot Big Bang epoch, including neutrino decoupling, nucleosynthesis and baryon acoustic oscillations (BAO), Decoupling of matter and radiation; Dark ages followed by structure formation; Existence of Dark matter, dominating gravitational dynamics at galactic to cluster scales; Existence of Dark energy, dominating cosmological scale gravitational dynamics at late times. 2.3 MAJOR QUESTIONS A series of major questions arise as regards the concordance model. 1. What are the cosmological parameters? A series of parameters characterize the standard cosmological model, and determine 7

8 important aspects of its nature (Tegmark, Zaldarriaga, and Hamilton 2001; Dodelson 2003, Spergel et al 2006). Massive new data sets are being collected that will refine them and decrease uncertainty as to their values. An important issue is how to break degeneracies, which has been well studied (Howlett et al 2012). 2. Is the universe open or closed? One key issue is whether the universe is open or closed, which actually is really two questions: (i) Is the spatial curvature parameter k positive, negative or zero? (ii) is the topology of the spatial sections in the universe the `natural simply connected topology, or something more complex? The first issue can be determined by sufficiently sensitive astronomical observations, determining the parameter Ω k = k/a 2 ; if k is positive, the universe has finite spatial sections if its geometry continues unchanged outside our past null cone. The second issue will not be determinable unless we live in a `small universe (see Section 3.1 below). The value of k is also key in the dynamics of the universe: for example it determines if a bounce is possible in the past, and recollapse in the future. 3. What do they tell us about inflation? The values of these parameters determine the ratio of tensor to scalar perturbations, and so give key information about the nature of inflation (Bond et al 2004, Ma et al 2010). They also test alternatives to inflation (Brandenberger 2009), but this is difficult because inflation is not a specific well defined theory: a large variety of alternative proposals create a lot of flexibility in what is possible, so it is difficult to disprove the whole family. 4. How did structure formation take place? Key elements of structure formation are understood: quantum perturbations generated in inflation lead to small inhomogeneities that generate baryon-acoustic oscillations leading to inhomogeneities on the last scattering surface, which then act as seeds allowing gravitational instability to generate structure in a bottom-up way after decoupling. But the details are unclear, particularly because as non-linearity sets in, complex astrophysical processes occur associated with reheating of matter. Additionally, an important issue is unresolved: we have the whole quantum-to-classical transition to account for, that is, how does quantum uncertainty give way to classical definiteness in the inflationary era? Current decoherence-based approaches to this question are insufficient to resolve the issue; this must necessarily involve some resolution of the measurement issue in quantum theory (see Sudarsky 2011 and references therein). This is a major lacuna in the physical explanation of structure formation in the early universe. 5. What is the nature of dark matter? We know that dark matter is non-baryonic, but do not know what it is; however potential candidates abound. Experimental and observational searches are under way to determine its nature. 8

9 6. What is the nature of dark energy? Existence of dark energy is established by observations of Type Ia supernovae, BAO, weak gravitational lensing, and the abundance of galaxy clusters. Particularly, decay of supernovae in distant galaxies provides a usable standard candle (maximum brightness is correlated to decay rate) that with redshifts gives a reliable detection of non-linearity in the redshift-distance relation, showing the universe is presently accelerating. Consequently cosmological dynamics is presently dominated an effective positive cosmological constant, with Ω Λ ~ 0.7. But its nature is completely unknown, indeed simple estimates of vacuum energy give the wrong answer by at least 70 orders of magnitude (Weinberg 1989). This is a major perplexity facing theoretical physics. 4 One possible resolution is some form of unimodular gravity, leading to a trace-free form of the Einstein equations (see Ellis, van Elst, Murugan, and Uzan 2011). 7. What happened at the start of the universe? It seems that there was a start of some kind to the present expansion epoch of the universe (as it is not in a steady state). What was the nature of this start? How did it happen? (insofar as we can meaningfully ask that question). 3. TESTING ALTERNATIVES It is general principle that one only fully understands what exists if you have a good idea of what does not exist: you don t understand the model you have unless you understand the alternatives. One should therefore ask, What else could be the case?, in order to understand what is. This is particularly true in the case of cosmology, where one can t go out and examine other physical examples of universes: one can however consider other hypothetical universes, and ask why they don t exist rather than the specific one we in fact happen to live in. In particular, different models may explain the same data there is a degeneracy in parameters with the same observational outcomes, for example - and we need to examine all the family that can explain the same data, in order to decide between them. It is not good enough to choose the first model that fits the data, when there may be many. 3.1 ALTERNATIVE TOPOLOGIES FLRW models can have closed finite spatial sections with complex topologies even if k=0 (locally flat) or k = -1 (locally negatively curved) (Ellis 1971a). While in general we can t tell what the topology of the spatial sections is, because they extend beyond our visual horizon, there is one exceptional case: we might possibly live in a small universes with closed spatial sections where the closure scale is less than the size of the visual horizon (Ellis and Schreiber 1986, Lachieze-Ray and Luminet 1995). In that case we can see right round the universe since decoupling, and can see many images of the same galaxy at different times in its history including our own. Local physics will be the 4 It is not however the most important problem in science, as some have claimed. 9

10 same as in the usual models, but there will be a large-scale cut off in wavelengths because of the compact topology. This is an attractive scenario in various ways, because these are the only cases where we can see the entire universe (Ellis and Schreiber 1986); but is quite difficult to test observationally. However it is in principle testable by source observation and by checking for identical circles in CMB sky (Cornish, Spergel, and Starkman 1998). Many simple cases have been excluded through such observations, but there remains a small possibility it may be true. If so it would be a major feature of the observed universe. It is a possibility that should indeed be fully observationally tested. 3.2 ANISOTROPIC (BIANCHI) MODES Another question is what difference can anisotropy make to dynamics and observations? This has been extensively investigated through use of the Bianchi spatially homogeneous but anisotropic models (Wainwright and Ellis 1996). Using such models one can put observational limits on early universe anisotropy, particularly by studying CMB anisotropies and element production in such universes. There is no evidence at present that there were indeed significant such anisotropies. But the point there is that one can t ask these questions unless you have such models. Indeed it is ironic that most papers on inflation say it can solve anisotropy and inhomogeneity issues, but only consider FLRW models. You can t derive that conclusion on this basis. 3.3 DARK MATTER AND MODIFIED GRAVITY One of the key issues is that dark matter is predicted to exist on the basis of astronomical observations, but is not yet understood. It is crucial to check that these observations do indeed indicate existence of dark matter, rather than that our theory of gravity is wrong. Consequently it is important to investigate alternatives such as MOND modified Newtonian dynamics, and its GR versions (Bekenstein 2012). There are a variety of such models, but they are restricted in various ways (Starkman 2012) One should note here that we get evidence on dark matter from gravitational dynamics in galaxies and clusters, from structure formation studies, and from gravitational lensing observations. Any theory must handle all these aspects. 3.4: DARK ENERGY AND INHOMOGENEITY One of the major problems for cosmology, and indeed theoretical physics, is the unknown nature of dark energy causing a speeding up of cosmological expansion at recent times (Weinberg et al 2012): Is it a cosmological constants? Is it quintessence (some dynamical form of matter?). What else might it be? And how are the observations compatible with estimates of the energy density of the quantum vacuum, some 70 to 120 orders of magnitude larger than the observed energy density? (Weinberg 1998) 10

11 Again one needs to investigate the possibility that the observations test a breakdown in General Relativity Theory rather than existence of dark energy, and many investigations are under way considering possible modifications of GRT that could account for the observations, such as including higher order terms in the Lagrangian. But given the significance of the problem, one needs to explore all possible other routes for explaining the observations. It is therefore of considerable importance that there are geometrical models that in principle can explain the data without any need for any modification of gravity, or any exotic physics. Because we observe spherical symmetry around us to high accuracy, we need to use spherically symmetric (Lemaître-Tolman-Bondi) models where we are somewhere near the centre. Now many people don t like this philosophically, but that s too bad: if the observations say that is the way things are, we have to accept it, and adjust our philosophy to fit the facts. So can we observationally put limits on late universe inhomogeneity? Can we test the Copernican Principle (the assumption we are at a typical place in the universe) rather than taking it as an untestable philosophical a priori assumption? Can we do away with dark energy through inhomogeneous models? The answer is that in principle this is indeed all possible. The SN data could be revealing inhomogeneity violating the Copernican Principle on close to Hubble scales. Such models are able to explain the SN observations: that s a theorem (Mustapha, Hellaby and Ellis 1999). So can such models explain the rest of the data of precision cosmology? Maybe, maybe not. A variety of tests have been developed based on Supernova observations down the past null cone (Clarkson, Bassett and Lu, 2007), Relating CBR anisotropies and BAO measurements in such models (Clarkson and Maartens 2010), Based on the kinematic Sunyaev-Zeldovich effect (Clifton, Clarkson and Bull, 2012). The latter test in effect enables one to see the interior region of the CMB 2-sphere on the LSS (see Figure 3) because of the scattering of radiation by hot gas that underlies the ksz effect. Thus it in essentials is an observational implementation of the `almost-egs theorem (Stoeger, Maartens and Ellis 1995) that proves a FRW geometry exists if the CMB radiation is almost isotropic everywhere in an open neighborhood of a point. Insert Figure 3 here: Testing homogeneity via the KSZ effect Another possibility is Uniform Thermal Histories: Testing that distant matter we observe has the same thermal history as nearby matter, resulting in the same kinds of structures being formed in distant regions as nearby (Bonnor and Ellis 1986). Tests of distance element abundances fall in this category (see Section 4.5 below). 11

12 Now some people claim these tests are unnecessary: it is philosophically implausible we live in such a universe, and so a waste of time checking the Copernican (homogeneity) principle. I completely disagree. A set of testable alternatives exists, leading to interesting observational proposals; it is important to do these tests, both because the CP is the foundation of standard model, and if it is not valid one can possibly do away with need for Dark Energy one of the key mysteries in present day cosmology. These tests have the effect of turning a previously untested a priori philosophical assumption at the foundations of standard cosmology into a scientifically testable hypothesis. I regard that as a big step forward: it is good physics and good science. Philosophical assumptions may or may not be true: we should test them whenever we can. 4 TESTING CONSISTENCY These tests can be regarded as consistency tests for the standard model. Because of the uniqueness of the universe as discussed above, consistency tests are of crucial importance: we should check our models for consistency in all possible ways (a philosophical point with implications for scientific practice). I list here further such tests AGES: IS THE UNIVERSE OLDER THAN ITS CONTENTS? This is perhaps the most crucial test of all: if it comes out wrong, it has the capacity to destroy the standard model. Indeed this is Hubble never believed in the idea of an expanding universe: the value of the Hubble Constant that he attained was wrong, and this test came out inconsistent with the FLRW models of his time. With present Hubble constant estimates, this works out acceptably. But it is crucial to keep checking as estimates of ages change CBR-MATTER DIPOLE AGREEMENT The standard interpretation of the CMB dipole anisotropy is that it is due to our motion relative to the cosmic rest frame defined by the CMB. A consequence is that there must be a parallel dipole in number counts of all classes of astronomical objects: radio sources, for example (Ellis and Baldwin 1984). If this dipole agreement were not to exist, it would call into question the cosmological interpretation of either the relevant sources, or the CMB. It would undermine the whole of the standard model if the CMB were not of cosmological origin (as suggested for example by the quasi-steady state theory). The sensitivity and statistics are difficult, but it seems this test is Ok COSMIC DISTANCE-DUALITY RELATION A key feature of standard models is the cosmic distance duality relation, also known as the reciprocity theorem (Ellis 1971). This underlies the standard (M,z) relation, CMB intensity observations, and gravitational lensing intensity observations. If it were not true, then the foundational assumption that observations are based on photons moving on null geodesics in a Riemannian spacetime would be proved wrong. 12

13 Tests are indeed possible, for example Khedekar and Chakrabort (2011) report one based on HI mass functions, and Holanda, Goncalves, and Alcaniz (2012) propose a test using measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich and X ray surface brightness observations. They find no significant violation of the distanceduality relation CBR TEMPERATURE AT A DISTANCE If the standard interpretation of the CMB is right, its temperature must change with redshift according to the formula T(z) = T 0 (1+z). Hence we need to find distant thermometers to measure the CMB temperature at significant redshifts. One such thermometer is interstellar molecules (Meyer 1994); it turns out one can also use the Sunyaev Zeldovich effect to test this relation (Avgoustidis et al 2011). This again is an important test: it checks that the CMB is what it is believed to be, rather than some local effect. So far this too is working out OK PRIMORDIAL ELEMENT ABUNDANCES WITH DISTANCE If the universe is spatially homogeneous then element production must also be spatially homogeneous, so primordial element abundances for galaxies at high z should be the same as nearby. This seems to be the case, although there is some query as regards Lithium; if that problem persists, it could be an indication of an inhomogeneous universe (Regis and Clarkson 2010). The importance of this test is that it checks conditions at very early times long before the LSS far out from our world line (see Figure 4). This is a special case of tests of uniform thermal histories for distant matter (Section 3.4). Insert Figure 4 here: Nucleosynthesis far out is tested by primordial element abundances. 5 THE UNIQENESS OF THE UNIVERSE As mentioned in Section 1.1, the key feature that separates cosmology from all other sciences is the uniqueness of the universe. There is only one object to look at; there is no similar object to compare it with. We can of course investigate almost countless aspects of the universe; but they are all aspects of one single object, the single universe domain we can observe. It s not just that we can t observe other universes: we also can t experiment on other universes, nor rerun this one. We have one unique object with one unique history that we want to understand. No other science has this nature. It is at this point that we inevitably move from more technical issues to more philosophical ones. 5.1 THE PHILOSOPHY OF THE HISTORICAL SCIENCES Now there are many other historical sciences (for example, the origin of the Galaxy, the origin of the Solar System, and the origin of life on Earth), and the way they relate to 13

14 theory is different than the experimental sciences, which is why they are often so much more controversial. But in all the other cases there are at least in principle other examples we can consider and about which we can one day hope obtain data (the most difficult example being the origin of life, but that may have occurred elsewhere in the universe. This is not the case as concerns cosmology. It is the unique historical science: hence we need to extract all evidence we can, and check our theories in all possible ways, as discussed above. But there are further consequences we now look at. The issue in all historical sciences is the tension between general laws and specific applications: how does one relate the influence of universal aspects (necessity) to that of contingent events (chance)? What is the role of specific initial conditions, as against that of general laws of universal validity? This leads to the question Is chance a genuine causal category, or is it just a code word for the fact that although everything is fully determined, we just don t have the necessary data? It is often treated as if it is a genuine causal factor, as in Monod s famous book Chance and Necessity (Monod 1972), but this is a very strange concept of a cause. Not knowing what the cause is, is not a very compelling cause! But this is to do with the issue of emergence of higher levels of structure, with coarse graining leading to a loss of lower level information (see section 8.2); in that context it can be regarded as a valid type of causation, because we have a level of description which excludes detailed lower level information. However in cosmology one is trying to model all there is; is it legitimate in that context? This is crucially tied in to the issue of the scale of modeling, mentioned above; but it also relates to the issue of determination by unique initial data, rather than generic laws Chance as a causal category'' is discussed by Hoefer (2010). Epistemologically there is really not a problem there chance'' just stands for causes we are unable to discern or determine. We don't know enough. Apparently, however, some philosophers in the past (e.g. Thomas Aquinas) considered ontological chance as a genuine causal category. 5 The specific situation where this matters is the idea of cosmic variance: the difference between what our statistical set of models predicts, and the specific unique outcome we actually encounter. In particular, the observed CBR angular power spectrum is significantly lower at large angles than predicted by theory. The issue is whether this large angle discrepancy between theory and observation is in need of an explanation, or is it just a statistical fluke due to chance that needs no explanation? This is a philosophical question that gains a bit of bite because just such a cut-off at large angular scales is predicted to occur in small universes (Section 3.1 above). The usual assumption is that it s just a statistical fluke. Starkman et al (2102) discuss other such anomalies in the CBR observations. 5 I thank Bill Stoeger for comments on this issue. Quantum theory raises specific issues in this regard I will not consider here. 14

15 The deeper issue in this regard is the common assumption that the universe should not be fine tuned : it is taken for granted that it should in some sense be of a generic nature. This is a complete philosophical change from what was taken for granted in cosmology up to the late 1970 s: before then it was taken for grated the universe had a very special nature. This was encoded in the idea of a Cosmological Principle, taken as a foundational presupposition of cosmology (Bondi 1960). The pendulum has swung to the opposite extreme, with people searching for all sorts of explanations of fine tuning. But no physical law is violated by any fine tuning there may be. Improbability of existence of fine tuning is a perfectly valid argument as regards multiple entities that occur in the universe and are subject to statistical laws; but there is no possible evidence or proof that the universe itself is subject to any such laws. So a key philosophical question is, Is the universe probable? This is an untestable philosophical assumption underlying much present day work, presumably based in the idea of probability in an ensemble of possibilities. But if only one universe is realised, this ensemble is hypothetical rather than actual, and there is no conclusive reason that it should be probable: the requisite ensemble for that argument does not exist. Maybe the universe IS fine tuned! - indeed there is a lot of evidence this is indeed the case (see the discussion of the Anthropic Coincidences below.) Whatever one s attitude, one should recognise that the concept of fine tuning is a philosophical issue. This illustrates how cosmology is a unique topic in physical science. 5.2 LAWS AND INITIAL CONDITIONS The further key point arising is that because of the uniqueness of the universe, it is not clear how to separate Laws (generic relations that must always be true) from initial conditions (contingent conditions that need not be true). Given the unique initial conditions that occurred in the one existing universe, We don t know what aspects of those initial conditions had to be that way, and what could have been different. Some relationships that locally appear to us to be fundamental physical laws my rather be the outcome of specific boundary or initial conditions in the universe: they could have worked out differently. The prime example is the existence of the second law of thermodynamics with a specific uniquely determined arrow of time. No choice of the arrow of time is determined by local fundamental physical laws, which (with one very weak exception) are time symmetric. It seems to be common cause nowadays that the unique one-way flow of time embodied in the crucially important second law of thermodynamics (Eddington 1928) is not after all a fundamental physical law: it is due to special initial conditions at the start of the universe (Ellis and Sciama 1972, Carroll 2010, Penrose 2011). Another example is the claim that the constants of nature fundamental determinants of local physics (Uzan 2011) -- are determined by the string theory landscape, and so may vary from place to place in the 15

16 universe. On this view, local physics is variable and context dependent (Rees 1999, Susskind 2006). Effective physical laws are then only locally valid (although determined by an underlying scheme that is globally valid). This is one of the drivers for searches to see if the constants of nature may vary with position in the universe (Uzan 2011). It must be emphasized that neither of these propositions can be proven to be the case; but certainly the first is widely believed as an outcome of tested physics, while the second is taken by many as being implied by plausible extrapolations of known physics. 6 MULTIVERSES: DENYING THE UNIQUENESS OF THE UNIVERSE One response to this situation is to deny the uniqueness of the universe: to claim we live in a multiverse (Carr 2009). Various motivations are given for this proposal: 1. It is claimed as the inevitable outcome of the physical originating process that generated our own universe, e.g. as an outcome of the chaotic inflationary scenario or of the Everett interpretation of quantum theory. 2. It is proposed as the result of a philosophical stance underlying physics: the idea that everything that can happen happens or whatever is possible is compulsory (the logical conclusion of the Feynman path integral approach to quantum theory). 3. It is proposed as an explanation for why our universe appears to be fine-tuned for life and consciousness, giving a probabilistic explanation for why we can exist. While the first is often claimed, it is the latter that has the most philosophical oomph. 6.1 FINE TUNING: THE ANTHROPIC ISSUE Examination of theoretically possible alternative universe models shows that there are many very specific restrictions on the way things are that are required in order that life can exist. The universe is fine-tuned for life, both as regards the laws of physics and as regards the boundary conditions of the universe (Barrow and Tipler 1986). A multiverse with varied local physical properties is one possible scientific explanation of this apparent fine tuning: an infinite set of universe domains with varying physics may allow almost all possibilities to occur, so that somewhere things will work out OK for life to exist just by chance (Rees 1999, 2001, Susskind 2006, Weinberg 2000, Carr 2009). Note that it must be an actually existing multiverse for this to work: this is essential for any such anthropic argument. As a specific example of the genre is Just Six Numbers by Martin Rees (1999). He explains that in order that life can exist, there must be fine tuning of the following physical constants: 1. N = electrical force/gravitational force = E = strength of nuclear binding = Ω = normalized amount of matter in universe = Λ= normalised cosmological constant =

17 5. Q = seeds for cosmic structures = 1/100, D = number of spatial dimensions = 3 He explains (Rees 1999), Two of these numbers relate to the basic forces; two fix the size and overall texture of our universe and determine whether it will continue for ever; and two more fix the properties of space itself These six numbers constitute a recipe for a universe. Moreover, the outcome is sensitive to their values: if any one of them were to be untuned, there would be no stars and no life An infinity of other universes may well exist where the numbers are different. Most would be stillborn or sterile. We could only have emerged (and therefore we naturally now find ourselves) in a universe with the right combination. This realization offers a radically new perspective on our universe, on our place in it, and on the nature of physical laws. Note that this assumes the basic structure of physics is unchanged; it is only the constants of physics that vary. This is a minimalist approach to the idea almost all possibilities occur : generically this could be much more broad (Tegmark 2004). What one assumes as possible is a philosophical choice, with no physical or observational test possible of whatever assumptions one makes. Rees focuses on only six parameters, but there are in fact many other physical constants that must be fined tuned if life is to be possible (Barrow and Tipler 1986, Ellis 2006). The particular important application of this idea is to explaining the small value of the cosmological constant ( dark energy ) by such an anthropic argument (Rees 1999, Weinberg 2000, Susskind 2006). Too large a positive value for Λ results in no structure forming and hence no life being possible; too large a negative value results in recollapse, with too short a lifetime for the universe to allow life to emerge. Thus anthropic considerations in a multiverse where Λ takes all possible values require that the value of Λ we observe will be small (in fundamental units), thus justifying the value we observe -- - different by 120 orders of magnitude from the value of the vacuum energy predicted by quantum field theory (Weinberg 1989). It provides a scientific explanation of this otherwise extremely implausible value. This example makes clear the true multiverse project: making the extremely improbable appear probable. It is a potentially viable explanatory model of such fine tuning in the universe domain we inhabit and observe.however even if a multiverse is assumed to exist, it is not clear that a meaningful probability measure is available, nor is it clear that that an infinite universe necessarily allows for all possibilities to occur (for a discussion, see Section 4.1 of Zinkernagel: 2011). The prospects for a viable explanation in probabilistic terms in this way are not fully secure. 17

18 6.2 TESTABILITY The key observational point however is that all the other domains considered in multiverse explanations are beyond the particle horizon (depicted in Figure 1) and are therefore unobservable. These observational limits are made clear in Figure 5. The assumption is we that can extrapolate from the observed domain to 100 Hubble radii, Hubble radii, or much much more: the word `infinity is casually tossed around in these writings, so that if we could see to 10 10,000,000 Hubble radii we would not even have started testing what is claimed -- and we can only see to 42 billion light years. Now this is an extraordinary claim. It is an explanation whose core feature is the assumption of huge numbers of entities as large as the entire visible universe that are in principle unobservable. The idea is that the theory (anthropic explanation of Λ in this way) is so good you should not worry about the basic causal feature of the theory being completely untestable. However some claim such a multiverse is implied by known physics, which leads to chaotic inflation (Linde 2003), with different effective physics necessarily occurring in the different bubbles of chaotic inflation (Susskind 2006). But this is not the case. The key physics (e.g. Coleman-de Luccia tunneling or the hypothesized inflaton potential, the string theory landscape) is extrapolated from known and tested physics to new contexts; the extrapolation is unverified and indeed is unverifiable; it may or may not be true 6. For example the parameter values that lead to eternal chaotic inflation may or may not be the real ones occurring in inflation, assuming it happened. And in particular the supposed mechanism whereby different string theory vacua are realised in different universe domains is speculative and untested. The situation is not Known Physics Multiverse, (1) as some writings suggest. Instead it is: Known Physics Hypothetical Physics Multiverse (2) Major Extrapolation The physics is hypothetical rather than established! This extrapolation is untested, and indeed may well be untestable: it may or may not be correct. The multiverse proposal is not based on known and tested physics. CAVEAT 1: A DISPROOF POSSIBILITY There is however one case where the chaotic inflation version of the multiverse can be disproved: namely if we observe that we live in a small universe, and have already seen 6 See for example 18

19 round the universe. In that case the universe is spatially closed on a scale we can observe, and the claimed other domains don t exist. As mentioned above (Section 3.1), we can test this possibility by searching for identical circles in the CBR sky. This is a very important test as it would indeed disprove the chaotic inflation variety of multiverse. But not seeing them would not prove a multiverse exists: their non-existence is a necessary but not sufficient condition for a multiverse. CAVEAT 2: A PROOF POSSIBILITY? The recent development of interest is the idea that proof of existence might be available through bubble collisions in the multiverse. Bubbles in chaotic inflation might collide if rate of nucleation is large relative to rate of expansion, and this might be observable in principle by causing recognisable circles in the sky, with different properties in their interior as opposed to the exterior. This is an intriguing idea, not withstanding the difficulties of predicting what would happen if spheres with different physics intersected each other. The clincher would be if one could demonstrate different values of some fundamental constants inside and outside such circles (Olive, Peloso, and Uzan 2011): that would vindicate the idea of different physics occurring in different domains, the core feature of a multiverse explanation. However not seeing them does not disprove the multiverse idea: these collisions will only occur in restricted circumstances in some multiverse instantiations. But this is certainly worth looking for: it is the only known observational test that would give genuine support to the physics of the multiverse proposal. 6.3 CRITERIA FOR A SCIENTIFIC THEORY Given that the multiverse proposal is not testable in any ordinary way, is it science? We need to consider what is the core nature of a scientific theory (a philosophical question). The kinds of criteria usually invoked are, 1. Satisfactory structure: (a) internal consistency, (b) simplicity (Ockham's razor), (c) beauty' or `elegance'; 2. Intrinsic explanatory power: (a) logical tightness, (b) scope of the theory --- unifying otherwise separate phenomena; 3. Extrinsic explanatory power: (a) connectedness to the rest of science, (b) extendability - a basis for further development; 4. Observational and experimental support: (a) the ability to make quantitative predictions that can be tested; (b) confirmation: the extent to which the theory is supported by such tests. It is the last two, and particularly the last, that characterizes a theory as scientific, in contrast to other types of theories that would like to be classed as scientific but are 19

20 rejected by mainstream scientists, such as Astrology or Intelligent Design. Their adherents claim they all satisfy the other criteria; it is predictive observational test and experiment, as well as separation from mainstream science, that separates recognised sciences from these claimants. Note 1: One must beware the non-uniqueness of Occam s razor and criteria of beauty. Is the multiverse idea beautiful? It depends on the eye of the beholder. Does it satisfy Occam s razor? Well one single entity (a multiverse) explains everything one wants to explain: the height of economy! But wait a minute: that one entity consists of uncountable billions of entire universe domains, each as large as the universe region to be explained, and each containing a huge number of galaxies, indeed often stated to be infinite. In this light it is a most extraordinarily extravagant postulation of innumerable unobservable universes all to explain one single entity (the observable universe). It hardly can be characterized as a law of parsimony. 7 Note 2: Our best physical theories allow various independent observations and experiments to constrain the theory. Agreement of such independent measurements of physical parameters is a much more demanding requirement than simple predictive success. Does the multiverse satisfy this criterion? No, because since it is assumed that anything whatever can happen in the various multiverse domains, a multiverse hypothesis can explain anything at all which means you can t disprove it by any particular observation, because it does not uniquely predict anything specific. There are some theories claiming that a multiverse predicts the universe must have open spatial sections (Freivogel et al 2006, Susskind 2006) but that only holds for some multiverse theories. The theories are extremely malleable. Some of them are constrained to obey the supposed possibilities of the string theory landscape but we don t know what these possibilities are, we don t even know if they include the physics we actually experience, and the status of this landscape proposal is disputed in the string theory community. Note 3: One might include as a criterion the way the conclusion is arrived at: for example the openness with which it is approached and the willingness to look at alternative explanations. In Lakatos terms, does it constitute a progressive scientific program? (Lakatos 1978). This raises very valid issues, but is hard to make precise and replicable; and while it is philosophically widely accepted, it is not an accepted criterion in the scientific community. The multiverse program is based on downgrading criterion 4 relative to the others; this is dangerous thing to do in that this amounts to a redefinition of what constitutes genuine science, because it is at the heart of the scientific method. This opens the door for all sorts of enterprises that are presently not considered as genuine science to be reclassified as true science. Multiverse adherents also claim it is strongly supported by criterion 3; but as noted above, the areas of physics that it is strongly linked to, such as string/m theory, are 7 Wikipedia: In his Summa Totius Logicae, i.12, Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora [It is futile to do with more things that which can be done with fewer]. 20

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